An Analysis of the Impact of Valve Closure Time on the Course of Water Hammer

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1 Archives of Hydro-Engineering and Environmenal Mechanics Vol. 63 (216), No. 1, DOI: /heem IBW PAN, ISSN An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer Aoloniusz Kodura Warsaw Universiy of Technology, Faculy of Building Services Hydro and Environmenal Engineering, Nowowiejska 2, -653 Warsaw, Poland (Received February 18, 216; revised May 23, 216) Absrac The knowledge of ransien flow in ressure ielines is very imoran for he designing and describing of ressure neworks. The waer hammer is he mos common examle of ransien flow in ressure ielines. During his henomenon, he ransformaion of kineic energy ino ressure energy causes significan changes in ressure, which can lead o serious roblems in he managemen of ressure neworks. The henomenon is very comlex, and a large number of differen facors influence is course. In he case of a waer hammer caused by valve closing, he characerisic of gae closure is one of he mos imoran facors. However, his facor is rarely invesigaed. In his aer, he resuls of hysical exerimens wih waer hammer in seel and PE ielines are described and analyzed. For each waer hammer, characerisics of ressure change and valve closing were recorded. The measuremens were comared wih he resuls of calculaions erfomed by common mehods used by engineers Michaud s equaion and Wood and Jones s mehod. The comarison revealed very significan differences beween he resuls of calculaions and he resuls of exerimens. In addiion, i was shown ha, he characerisic of buerfly valve closure has a significan influence on waer hammer, which should be aken ino accoun in analyzing his henomenon. Comarison of he resuls of exerimens wih he resuls of calculaions? may lead o new, imroved calculaion mehods and o new mehods o describe ransien flow. Key words: ime of valve closure, buerfly valve, ressure characerisic, ransien flow, waer hammer 1. Inroducion There are wo kinds of flow which can describe moion of liquids in ressure ielines. These are seady flow and ransien flow. Seady flow is very commonly used by engineers in calculaing arameers of ressure neworks. A model of seady flow consiss of simle equaions and can be used under mos condiions. The oher ye of flow, ransien flow, is raher rare, bu, due o raid changes in is velociy, can lead o significan roblems in he mainenance of ressure sysems.

2 36 A. Kodura The waer hammer is one of he forms of ransien flow. This erm is used o describe a ressure wave which was generaed by a raid change of flow velociy in a ieline (Ramos and de Almeida 22). Tha change in ressure is caused by he ransformaion of kineic energy ino ressure energy. A ressure wave sreads in he ieline wih high celeriy, which resuls in ineracions beween he liquid s recise bulk modulus, fricion forces and ineria forces, as well as arameers of he ie wall, such as he maerial s bulk modulus, hickness, diameer and lengh (Miosek 27, Sreeer e al 1998). The invesigaion of he waer hammer henomenon is imoran for science and for racical uroses. The racice of ressure sysem mainenance shows ha he number of breakdowns due o ransien flow in waer suly sysems is significan (Illin 1987). Moreover, he breakdowns resuling from waer hammer are usually exensive. This is he mos imoran reason for he large number of differen models and equaions used o calculae he main arameers of he henomenon, such as he exreme value of ressure, wave frequency, ime of duraion ec. One of he major roblems for mos mehods is he lack of exerimenal measuremen daa. For over a cenury, heoreical soluions have redominaed in invesigaions of he waer hammer henomenon. Generally, his henomenon can occur in wo siuaions: as a raid waer hammer, when he ime of closing he gae is shorer hen he reurn ime of he refleced wave, or as a comlex waer hammer, when he closure ime is longer han he reurn ime of he refleced wave (Sreeer e al 1998, Thorley 24). Theoreically, he relaionshi beween he closure ime and he reurn ime of he refleced wave makes i ossible o disinguish recisely beween wo kinds of he henomenon. Furhermore, he exension of he closure ime is one of he mos commonly used mehods for reducing he maximum ressure increase (or minimum ressure decrease) (Marcinkiewicz e al 28, Pires e al 24). However, his seemingly simle soluion deends on he arameers of differen kinds of gaes and valves. To dae, he influence of he kind of closure has seldom been analyzed. The main aim of his aer is o comare an exerimenal analysis of he waer hammer henomenon and heoreical mehods of deermining he maximum ressure increase. I should be menioned ha he influence of he ball valve characerisic on waer hammer was analyzed in a revious aricle (Kodura 211). This aer is he resul of he nex sage of invesigaions. Lis of symbols used in he aer a wave roagaion celeriy [m/s], h he head dro across he valve under he iniial seady flow condiions, which can be measured jus before he waer hammer henomenon occurs [m], L ieline lengh [m], ρ liquid densiy [kg/m 3 ],

3 An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer 37 T C gae clossure ime, C dimensionless valve closure ime [ ], T R reurn ime of he refleced wave, α arameer of iniial value of ressure losses during seady flow he beginning of he waer hammer henomenon, υ waer velociy change [m/s], υ velociy of seady flow before he beginning of he waer hammer henomenon [m/s]. 2. Theoreical Descriion of Comlex Waer Hammer 2.1. Basic Equaions As already menioned, he hisory of waer hammer henomenon invesigaions is quie long. In he firs equaion, Joukowsky (in 1898) ried o find a value of he maximum ressure change due o raid waer hammer (Wylie e al 1993): = υ ρ a, (1) where: υ = waer velociy change, ρ = liquid densiy, a = wave roagaion celeriy. Joukowsky s formula can be used o describe he maximum ressure increase (in ha case, he henomenon is called a osiive waer hammer) as well as he minimum ressure decrease (a negaive waer hammer). In he firs case, a sudden gae closing leads o an enormous ressure increase. In he second, waer hammer in he form of negaive ressure is a resul of a sudden acceleraion of waer (due o, for examle, a um saring or an oening of he gae). I should be noed ha Joukowsky s equaion can be used by engineers for maximum ressure change esimaion. The wave celeriy can be calculaed from he following equaion (Wylie e al 1993): a = 2 L T R, (2) where: L = ieline lengh, T R = reurn ime of he refleced wave. Theoreically, he ime of gae closure T C should be shorer han he reurn ime of he refleced wave for he raid waer hammer. The exension of he closure ime reduces he exreme ressure change. For a linear change in liquid velociy and if he oal ressure increase is less han 22% of ressure under seady condiions before waer hammer, he ressure increase is esimaed from Michaud s formula (Miosek 28): = 2 ρ υ L T C (3) where: υ = velociy of seady flow before he beginning of he waer hammer henomenon, T C = gae closure ime.

4 38 A. Kodura Eq. 3 is very similar o Joukowsky s formula Eq. 1 one difference is he relacemen of wave celeriy by he quoien 2L/T C. The resul of ha form is he assumion of linear velociy change, which is very difficul achieve. This formula does no consider he influence of gae characerisics, which is anoher very imoran deficiency of Michaud s equaion Wood and Jones s Mehod Wood and Jones were he nex researchers who ried o describe he influence of he gae on he ransien flow. Their idea was o inroduce wo arameers: dimensionless valve closure and dimensionless maximum ransien ressure change (Wood and Jones 1973, Thorley 24). The boundary assumion is ha Joukowsky s formula can be adoed as he bes equaion o calculae he maximum ressure change during a raid waer hammer. The resriced boundary beween raid and comlex waer hammer is sill he same. Only he value of he ransien ressure change can be calculaed from he knowledge of he iniial condiions of a head dro across he gae under he iniial seady flow. Wood and Jones develoed chars based on heoreical analysis of he mos common yes of valves (circular gae, globe, needle, square gae, buerfly and ball valve). Those chars, reresening individual valve yes, exress he relaionshi beween he dimensionless valve closure ime and dimensionless maximum ransien ressure change for very recisely described iniial condiions. The α arameer is used o describe he influence of he iniial condiions according o he equaion (Wood and Jones 1973): α = g h υ a, (4) where: h = he head dro across he valve under he iniial seady flow condiions, which can be measured jus before he waer hammer henomenon occurs, a = wave roagaion celeriy, υ waer velociy change. The α arameer deermines he value of he maximum ressure change. The unknown value has o be read from he char by using he α arameer and he dimensionless valve closure ime, which is described by he formula (Wood and Jones 1973): C = T C, (5) where: C = dimensionless valve closure ime. The value of he dimensionless maximum ransien ressure change, which can be read from he char, is relaed o he unknown maximum ransien ressure change (Wood and Jones 1973): m = 2 L a max υ ρ a, (6)

5 An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer 39 where: m = dimensionless maximum ransien ressure change, max = maximum ransien ressure head. Tha mehod, develoed by Wood and Jones, is a significan imrovemen in he heory of comlex waer hammer. However, here are also wo roblems, which have o be solved. Firs of all, he gae is described by a consan resisance coefficien, which is calculaed as for he seady flow. During he comlex waer hammer, he velociy across he valve is changeable, which can affec he resuls. The second roblem ignores fricion resisance in ransien flow. 3. Exerimenal Analysis 3.1. Model The Wood and Jones s mehod was develoed by heoreical analysis of ransien flow in ressure ielines. Over he years, he develomen of knowledge of course of waer hammer and he imac of he closure ime of he valve on he ressure increase has no been sufficienly exlained. In order o analyze he henomenon, a hysical model, shown in Fig. 1, was buil. The model consised of a ressure ieline (1) and a ressure ank (2) sulied from he waer nework (3). A he downsream end of he ie, a buerfly valve (4) wih a unique sysem for regisering he angle of closing in ime was insalled. Two ressure ransducers (5), locaed close o he valve, were conneced o a ersonal comuer (6) via an analog/digial card (7) o sore exerimenal daa. An addiional ball valve (8) was locaed downsream o ensure a consan value of discharge during seady flow. The discharge was measured by an elecro-magneic waer meer (9) D, e Q 4 Fig. 1. A skech of he exerimenal model Two series of exerimens were made. The firs series were carried ou in a 177 m long seel ieline wih an inernal diameer of 32 mm, and he second in a 24 m long HDPE ie wih an inernal diameer of 35 mm. In boh cases, he same buerfly valve was used. For each series, a leas 35 measuremens of waer hammer were erformed. The ime of valve closing was measured each ime. The idea was o measure waer hammer eisode for differen closing imes bu wih a linear funcion of valve closing. This assumion is similar o he Wood and Jones s model.

6 4 A. Kodura 3.2. Exerimenal Resuls The exerimenal daa were recorded in he form of ressure characerisics. Fig. 2 and Fig. 3 show samles of daa for he seel and HDPE ielines, resecively. Each characerisic was analysed, and he characerisic arameers of ransien flow were calculaed: valve closing ime, reurn ime of he refleced wave, wave frequency, and maximum ressure increase. As already menioned, he exerimens were made in wo series each for a differen maerial of he ieline. The idea was o deermine he influence of he buerfly valve closure characerisic on he ressure increase. A comarison beween he wo series makes i ossible o eliminae he influence of he ie maerial on he henomenon. A /A A /A,9 1,9 1,8 9,8 9,7,6 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 8 7,7,6 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 8 7,5 6,5 6,4 5,4 5,3 4,3 4,2 3,2 3,1 2, , , a) b),9 A/A 1,9 A/A 1,8 9,8 9,7,6 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 8 7,7,6 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 8 7,5 6,5 6,4 5,4 5,3 4,3 4,2 3,2 3,1 2, , , c) d) Fig. 2. Pressure characerisics for he seel ieline and he reurn ime of he refleced wave T R =.26 s: a) buerfly valve closure ime T C =.21 s < T R ; b) T C =.37 s > T R ; c) T C = 1.1 s > T R ; d) T C = 5.7 s > T R

7 An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer 41 Boh figures (Fig. 2 and Fig. 3) resen he resuls in he same way. A smooh solid line was used o reresen ressure jus usream of he buerfly valve. A fine doed line was used o illusrae ressure jus downsream of he valve. The hird, dashed line reresens he closure angle of he gae. Tha line exresses he emorary cross-secion of he buerfly valve during closure.,9 A/A 1,9 A/A 1,8,7 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 9 8,8,7 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 9 8,6 7,6 7,5 6,5 6,4 5,4 5,3 4,3 4,2 3,2 3,1 2, , , a) b),9 A/A 1,9 A/A 1,8,7 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 9 8,8,7 P1 - ressure characerisic P2 - ressure characerisic Valve closure characerisic 9 8,6 7,6 7,5 6,5 6,4 5,4 5,3 4,3 4,2 3,2 3,1 2, , , c) d) Fig. 3. Pressure characerisics for he HDPE ieline and he reurn ime of he refleced wave T R = 1.3 s: a) buerfly valve closing ime T C =.95 s < T R ; b) T C = 1.35 s > T R ; c) T C = 2.67 s > T R ; d) T C = 23.7 s > T R For he seel ieline, he iniial measuremens of velociy during seady condiions was comared for each measured series and equalled.32 m/s. The reurn ime of he refleced wave was.26 s. In he case of he HDPE ieline, he iniial velociy was equal o.5 m/s, and he reurn ime of he refleced wave was 1.3 s. Fig. 2 and Fig. 3 show examles of differen relaionshis beween he closure ime and he reurn ime of he refleced wave. The firs lo in boh figures rere-

8 42 A. Kodura sens a raid waer hammer henomenon. The oher los illusrae comlex waer hammers, in which he closure ime is longer hen he reurn ime of he refleced wave Comarison wih Common Theoreical Mehods The nex se was o comare he exerimenal daa wih he resuls of heoreical mehods. For each closing ime, he maximum ressure increase was calculaed by Michaud s equaion. The oher heoreical mehod used for comarison was Wood and Jones s mehod. For each colleced characerisic, he measured head dro across he valve was used o calculae he α arameer. Nex, he roer curve from Wood and Jones s char was chosen. For he seel ieline, he α arameer is.5, and for he HDPE ieline he α arameer equals.1. The resuls are shown in Fig. 4 and Fig. 5. Dimensionless maximum ransien ressure change m 1,1,1 Grah 1 alfa =,5 buerfly valve seel ieline Michaud equaion, Dimensionless valve closure ime c Fig. 4. Comarison of he exerimenal daa wih he resuls of calculaions by Michaud s equaion and Wood and Jones s mehod for he seel ieline The exerimenal daa are reresened by filled circles. The resuls from Michaud s equaion are marked by emy circles. Wood and Jones s mehod is illusraed by α curves. The X axis reresens he dimensionless valve closure ime, and he Y axis exresses dimensionless maximum ressure change. I is worh noing ha he exerimenal daa shown in boh figures are locaed in oally differen areas of he char. For boh ielines he measured values of he

9 An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer 43 Dimensionless maximum ransien ressure change m 1,1,1 Grah 1 alfa =,1 buerfly valve HDPE ieline Michaud equaion, Dimensionless valve closure ime c Fig. 5. Comarison of he exerimenal daa wih he resuls of calculaions by Michaud s equaion and Wood and Jones s mehod for he HDPE ieline maximum ressure change are significanly bigger han hose calculaed by Michaud s formula as well as by Wood and Jones s mehod. In fac, he laer heoreical mehod yields greaer ressure increase values han Michaud s formula, bu he difference beween calculaion resuls and measuremens is significan in his case as well. Three remarks need o be made a his oin. Firs of all, Michaud s equaion gives unrealisically small values of ressure increase and should no be used for calculaion or esimaion of ressure increase during waer hammer. Second, Wood and Jones s mehod leads o more realisic values of ressure increase, bu he resuls of calculaions are sill significanly smaller han he measured values. The hird remark concerns he heory of waer hammer: he boundary beween raid and comlex waer hammer is no very shar. Exending he closure ime reduces he maximum ressure increase, bu he relaionshi is differen han described by Michaud s equaion. From he racical oin of view, he influence of closing ime exension can be significan only when he closure ime is aroximaely 1 imes as long as he reurn ime of he refleced wave. The analysis of he above resuls leads o he quesion abou he influence of he valve ye on waer hammer henomenon. A comarison of exerimenal daa colleced during waer hammer in a seel ieline and a HDPE ieline equied wih ball valves is shown in Fig. 6 and Fig. 7, resecively. For he seel ieline, differences beween waer hammer caused by he ball valve and he buerfly valve are no

10 44 A. Kodura Dimensionless maximum ransien ressure change m 1,1,1 Grah 1 buerfly valve seel ieline ball valve seel ieline, Dimensionless valve closure ime c Fig. 6. Comarison of exerimenal daa colleced during waer hammer in seel ielines wih a ball valve (Kodura 211) and a buerfly valve Dimensionless maximum ransien ressure change m 1,1,1 Grah 1 buerfly valve HDPE ieline ball valve HDPE ieline,1 h] Dimensionless valve closure ime c Fig. 7. Comarison of exerimenal daa colleced during waer hammer in HDPE ielines wih a ball valve (Kodura 211) and a buerfly valve

11 An Analysis of he Imac of Valve Closure Time on he Course of Waer Hammer 45 very significan. When he closing ime is shorer han 1% of he reurn ime of he refleced wave, he buerfly valve roduces a slighly higher ressure increase. For longer closure imes, waer hammer due o buerfly valve closing has slighly smaller values han ha due o he ball valve. In he case of he HDPE ieline, he relaionshi is similar, bu he difference beween waer hammers caused by he ball valve and he buerfly valve is bigger. 4. Conclusion The waer hammer henomenon sill has no been recisely defined in heory and described by he exising equaions. A significan lack of exerimenal daa leads o inadequae heoreical models. The commonly used Michaud s equaion significanly underesimaes ressure increase and herefore should no be used. Alhough he main idea of Wood and Jones s mehod of inroducing he valve ye is correc, his mehod sill leads o esimaes lower han he acually observed values. By aking ino accoun only he valve ye and iniial seady head losses i is sill imossible o describe he henomenon roerly. The roblem should herefore be invesigaed exerimenally. From he racical oin of view, he maximum ressure increase for a closure ime shorer han 25% of he reurn ime of he refleced wave can be calculaed by Joukowsky s formula. References Ilin J. A. (1987) Calculaions of waer sysems, Sroizda, Moscow (in Russian). Kodura A. (211) Influence of characerisic of ball valve closing on waer hammer run, Proceedings of he Twelfh Inernaional Symosium on Waer Managemen and Hydraulic Engineering, Gdańsk, Poland. Marcinkiewicz J., Adamowski A., Lewandowski M. (28) Exerimenal evaluaion of abiliy of Rela5, Drako, Flowmaser2 TM and rogram using unseady wall fricion model o calculae waer hammer loadings on ielines, Nucl Eng Des, 238, (8), doi:1.116/j.nucengdes Miosek M. (27) Fluid Mechanics in Environmenal Engineering, WNT Warsaw, (in Polish). Pires L. F. G., Laidea R. C. C., Bareo C. V. (24) Transien Flow Analysis of Fas Valve Closure in Shor Pielines, Proceedings of Inernaional Pieline Conference, Ocober 4 8, 24, Calgary, Albera, Canada. Ramos H., de Almeida B. A. (22) Parameric Analysis of Waer Hammer Effecs in Small Hydro Schemes, Journal of Hydraulic Engineering, 128 (7), Sreeer V. L., Wylie B. E., Bedford K. W. (1998) Fluid Mechanics, WCB McGraw-Hill, New York. Thorley A. R. D. (24) Fluid ransiens in ieline sysem: a guide o he conrol and suression of fluid ransiens in liquids in closed conduis, ASME Press, New York. Wood D. J., Jones S. E. (1973) Waer-hammer chars for various yes of valves, Journal of Hydraulic Division, 99 (1), Wylie B. E., Sreeer V. L., Suo L. (1993) Fluid Transiens in Sysems, Englewood Hills New Jersey, Prenice Hall.